They can be canon, crack, or killed by one of the Erins!
Honestly, I think my favorite ship is still Cloudtail and Brightheart. It's been my favorite shipping since I started reading the series, and it's one of the only happy pairings that the Erins haven't killed yet...
I'm also a fan of Dustpelt and Ferncloud, despite not really liking either character. I just really adore how they interact and I think how they handled
the post-death of Ferncloud in Bramblestar's Storm was amazing. Coming from someone who's not only lost a significant other, I've also had depression, and I think they really nailed that with Dustpelt. It's a really important ship to me because it shows that love is forever, even if your partner isn't around anymore...because you'll see them again one day.
Also a really huge fan of Turtle Tail and Gray Wing, even though
Turtle Tail is dead and they apparently included Slate to be his new mate and all that nonsense.
Sorreltail and Brackenfur is another one of my favorite ships,
but, alas, it has gotten sent to the gallows by Vicky.
For non-canon ships, I'm really liking Thunder and Lightning Tail, Tallstar and Jake (why is this not canon), and Hollyleaf and Fallen Leaves. I also used to ship Hollyleaf and Sol and I'm not sure why.... I will also happily ship Dovewing and Bumblestripe, and Ivypool and No One Because She Is Awesome Without a Mate